Wednesdays, 5pm-6pm, 891 Evans Hall
The Applied Algebra Seminar is an interdisciplinary seminar on applications of algebra to fields outside mathematics. Our goal is to connect mathematicians with researchers from other fields using algebraic tools in their work.
Talks are aimed at an interdisciplinary graduate student audience including mathematicians, computer scientists, engineers, biologists, economists, statisticians, and more.
Please sign up for the seminar mailing list to receive information about applied algebra happenings around campus. You can also contact the organizers to be added to the mailing list.
September 14 - Martin Helmer, UC-Berkeley (Math)
Nearest Points on Toric Varieties
We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point. This also leads to expressions for the polar degrees and Chern-Mather class of a projective toric variety. This is joint work with Bernd Sturmfels.
September 21 — Anna Seigal, UC-Berkeley (Math)
Real Rank Two Geometry
The real rank two locus of an algebraic variety is the union of all secant lines spanned by real points. We seek a semi-algebraic description of this set and its boundary. Our study of Segre and Veronese varieties yields a characterization of tensors of real rank two. This is joint work with Bernd Sturmfels.
October 26 - Emily Clader, (SFSU)
Double ramification cycles and tautological relations
Tautological relations are certain equations in the Chow ring of the moduli space of curves. I will discuss a family of tautological relations, first conjectured by A. Pixton, that arises by studying moduli spaces of ramified covers of the projective line, and I will describe how these relations can be used to recover a number of well-known facts about the moduli space of curves.
This is joint work with S. Grushevsky, F. Janda, and D. Zakharov.
November 30 - Justin Chen, (UC-Berkeley)
Numerical Implicitization for Macaulay2
Many varieties of interest in algebraic geometry and applications are given as images of regular maps, i.e. via a parametrization. Implicitization is the process of converting a parametric description of a variety into an intrinsic (i.e. implicit) one. Theoretically, implicitization is done by computing (a Grobner basis for) the kernel of a ring map, but this can be extremely time-consuming -- even so, one would often like to know basic information about the image variety. The purpose of the "NumericalImplicitization" package is to allow for user-friendly computation of the basic numerical invariants of a parametrized variety, such as dimension, degree, and Hilbert function values, especially when Grobner basis methods take prohibitively long.